Quantum-Transport Study on the Impact of Channel Length and Cross Sections on Variability Induced by Random Discrete Dopants in Narrow Gate-All-Around Silicon Nanowire Transistors

In this paper, we review and extend recent work on the effect of random discrete dopants on the statistical variability in gate-all-around silicon nanowire transistors. The electron transport is described using the nonequilibrium Green´s function formalism. Full 3-D real-space and coupled-mode-space repre sentations are used. Two different cross sections (i.e., 2.2 × 2.2 and 4.2 × 4.2 nm²) and two different channel lengths (i.e., 6 and 12 nm) have been considered. The resistivity associated with discrete dopants can be estimated from the averaged current-voltage characteristics. The threshold-voltage variability and the sub threshold-slope variability are reduced greatly in the transistors with longer channel length. Both are smaller at equivalent channel lengths in the 2.2 × 2.2 nm² device due to better electrostatic integrity. At the same time, the ON-state-current variability associated with the varying resistance of the access regions is virtually independent of the channel length. However, it is reduced greatly in the 4.2 × 4.2 nm² transistor due to a fourfold increase in the number of dopants in the access regions and corresponding self-averaging effects. Finally, we present results for the smallest transistor combining two sources of variability (i.e., discrete random dopants and surface roughness) and phonon scattering.